• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.341-345
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• 2007

In this paper we show that the second order mock theta function, given by Hikami, is bounded and satisfies the second condition for the mock theta functions.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.767-777
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• 2007

By proving a summation formula, we enumerate the expansions for the mock theta functions of order 2 in terms of partial mock theta functions of order 2, 3 and 6. We show a relation between Ramanujan's ${\mu}(q)$-function and his sixth order mock theta functions. In addition, we also give the continued fraction representation for ${\mu}(q)$ and 2nd order mock theta functions and $Pad\acute{e}$ approximants.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.87-97
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• 2017

In [9], we computed shadows of the second order mock theta functions and showed that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. In this paper, we further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.117-129
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• 2005

We give a generalization of bilateral mock theta functions of order eight and show that they are $F_q$-functions. We also give an integral representation for these functions. We give a relation between mock theta functions of the first set and bilateral mock theta functions of the second set.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.889-900
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• 2005

We consider the second order mock theta functions defined by McIntosh and define generalized functions. We give integral representation and multibasic expansion of these functions. We also show that they are $F_q$-functions.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2155-2163
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• 2017

Zwegers showed that a mock theta function can be completed to form essentially a real analytic modular form of weight 1/2 by adding a period integral of a certain weight 3/2 unary theta series. This theta series is related to the holomorphic modular form called the shadow of the mock theta function. In this paper, we discuss the computation of shadows of the second order mock theta functions and show that they share the same shadow with a mock theta function which appears in the Mathieu moonshine phenomenon.